Homework SourseA manufacturing firm employs three analytical plans for desi
A manufacturing firm employs three analytical plans for design and development of a particular product. For cost reasons, all three plans are used at varying times. In fact, plans A, B, and C are used for 30%, 20%, and 50% of the products, respectively. It is also known from past experience that 2% of the products made using plan A will be defective. Similarly, the product defective rate for plan B and C are 3% and 1%, respectively. (a) Suppose that a finished product is randomly selected. What is the probability that it will be defective? (b) If a randomly selected product is found to be defective, which plan was most likely used? Clearly explain your answer
Solution
By using the Bayes Probability Law
(a) 0.017
(b) Plan C was most likely used.
| Event | Prior Prob. | Conditional Prob. | Joint Prob. | Posterior Prob. |
| A | 0.3 | 0.02 | 0.006 | 0.3529 |
| B | 0.2 | 0.03 | 0.006 | 0.3529 |
| C | 0.5 | 0.01 | 0.005 | 0.2942 |
| Total | 0.017 |
